Novel Generalized Low-Pass Filter with Adjustable Parameters of Exponential-Type Forgetting and Its Application to...

Area of Science:

• Signal Processing
• Mathematical Filtering Techniques

Background:

• Classical Gaussian filters are widely used but have limitations in certain signal processing applications.
• The Mittag-Leffler function offers unique properties for modeling complex phenomena.

Purpose of the Study:

• Introduce a novel Mittag-Leffler filter.
• Evaluate its performance against traditional Gaussian filters.
• Demonstrate its application in real-world signal denoising, specifically for ECG signals.

Main Methods:

• Developed a new filter by incorporating the Mittag-Leffler function into the probability-density function and convolution kernel.
• The filter incorporates three parameters, including a filter-forgetting factor, to adjust curve shape.
• Illustrative examples and real ECG signal denoising were used for evaluation.

Main Results:

• The Mittag-Leffler filter shows significant advantages over classical Gaussian filtering techniques.
• Effective denoising of real ECG signals was achieved using the proposed filter.
• The filter's adjustable parameters allow for flexible curve shaping.

Conclusions:

• The proposed Mittag-Leffler filter is a viable and advantageous alternative to Gaussian filters for signal processing.
• It shows particular promise for denoising noisy ECG signals.
• Implementation details and a MATLAB function are provided for practical use.